Combine the cream cheese, mascarpone, milk, powdered sugar, and vanilla in the bowl of an electric mixer. Mix on a medium speed for 1 minute, stopping to scrape down the sides of the bowl as necessary. You want the mixture to be runny enough to be easy to pour. Add more milk if necessary.
Assemble the popsicles, starting by adding the raspberries to the popsicle molds. Gently crush them to get them to fit in place.
Then pour the cream cheese and mascarpone mixture over the raspberries. Fill the popsicles molds until the mixture is 1 inch from the top of the mold.
Add half of the blackberries. Use a fork to crush the rest, and then pour the crushed blackberries into the molds until they are full.
Place the handles in the molds, and let the popsicles freeze overnight.